They did share many things and since both divorced they probably supported each other in difficult times. If the press and the rivalry they've created between her hadn't been so bad, I'm sure their friendship would have lasted longer. I don't think hatred took place in their feelings but it was more like a ruthless competition after their row.
While making some research on Sarah, I came across a terrible article saying that the Duchess had conveyed to
Madame Vasso many intimate details about Diana's lovelife. Of course she didn't talk against her will then but she wasn't aware that the psychic healer would reveal everything in her book :
Fergie: The Very Private Life of the Duchess of York. I think this "unwilled" betrayal actually broke the ladies' friendship. From what I've read in the article, the content was really, really embarrassing. I have the address of the article but I'm not sure members here would like to read this piece of garbage.